arXiv subjects

I. M. Sokolov

Publications and source records attributed to I. M. Sokolov.

117 records · Page 7Linked to original sources

arXiv2001

Thermodynamics and Fractional Fokker-Planck Equations

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the FFPEs describe the system whose noise in equilibrium funfills the Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions of the corresponding FFPEs are probability densities for all cases where the solutions of normal Fokker-Planck equation (with the same Fokker-Planck operator and with the same initial and boundary conditions) exist. The solutions of the FFPEs for superdiffusive dynamics are not always probability densities. This fact means only that the corresponding kinetic coefficients are incompatible with each other and with the initial conditions.

cond-mat.stat-mech↗

arXiv2000

Does strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation towards the Boltzmann equilibrium distribution. The properties of the Levy-flight FFPE derived here are compared with earlier findings for subdiffusive FFPE. The latter is characterized by a non-exponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached and modifications of the Boltzmann thermodynamics are not required.

cond-mat.stat-mech↗

arXiv2000

Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time-protocols of the outer force exist under which the operation is reversible and the ideal value of efficiency is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures.

cond-mat.stat-mech↗

arXiv2000

Statistics of two-particle dispersion in two-dimensional turbulence

We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in good agreement with the original Richardson's description in terms of diffusion equation. The deviations are only of the quantitative nature. These deviations, and the observed strong sensitivity to the finite size effects, are associated with the long-range-correlated nature of the particles' relative motion. The correlation, or persistence, parameter is measured by means of a Lagrangian ``turning point'' statistics.

nlin.CD↗

arXiv2000

Levy flights from a continuous-time process

The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW), dual to usual Scher-Montroll model, in which $n$ grows sublinearly with t. The models in which Levy-flights emerge due to a temporal subordination let easily discuss the response of a random walker to a weak outer force, which is shown to be nonlinear. On the other hand, the relaxation of en ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal Boltzmann distribution. The mixed models, describing normal CTRW in superlinear operational time and Levy-flights under the operational time of subdiffusive CTRW lead to paradoxical diffusive behavior, similar to the one found in transport on polymer chains. The relaxation to the Boltzmann distribution in such models is slow and asymptotically follows a power-law.

cond-mat.stat-mech↗

arXiv2000

Small-World Rouse Networks as models of cross-linked polymers

We use the recently introduced small-world networks (SWN) to model cross-linked polymers, as an extension of the linear Rouse-chain. We study the SWN-dynamics under the influence of external forces. Our focus is on the structurally and thermally averaged SWN stretching, which we determine both numerically and analytically using a psudo-gap ansatz for the SWN-density of states. The SWN stretching is related to the probability of a random-walker to return to its origin on the SWN. We compare our results to the corresponding ones for Cayley trees.

cond-mat.stat-mech↗

arXiv2000

Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and for Cayley trees.

cond-mat.stat-mech↗

arXiv2000

Ideally Efficient Irreversible Molecular Gears

Typical man-made locomotive devices use reversible gears, as cranks, for transforming reciprocating motion into directed one. Such gears are holonomic and have the transduction efficiency of unity. On the other hand, a typical gear of molecular motors is a ratchet rectifier, which is irreversible. We discuss what properties of rectifier mostly influence the transduction efficiency and show that an apliance which locks under backwards force can achieve the energetic efficiency of unity, without approaching reversibility. A prototype device based on ratchet principle is discussed.

cond-mat.stat-mech↗

arXiv1999

Two-Particle Dispersion in Model Velocity Fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to $v^{2}(r)\propto r^α$ and the corresponding correlation time scales as $τ(r)\propto r^β$, and fix $α=2/3$, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For $α/2+β< 1$ the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, $α/2+β>1$, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation.

chao-dyn↗